Question: Reduce to lowest terms: $ \dfrac{1}{9} \div - \dfrac{5}{8} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{8}$ is $- \dfrac{8}{5}$ Therefore: $ \dfrac{1}{9} \div - \dfrac{5}{8} = \dfrac{1}{9} \times - \dfrac{8}{5} $ $ \phantom{ \dfrac{1}{9} \times - \dfrac{8}{5}} = \dfrac{1 \times -8}{9 \times 5} $ $ \phantom{ \dfrac{1}{9} \times - \dfrac{8}{5}} = \dfrac{-8}{45} $